For a time there was only speculation how backdoors are being implanted to weaken encryption and to subvert trust in secure online communication.
There are a number of requirements a good backdoor has to meet to become an efficient surveillance tool for the NSA and other like-minded organisations.
First, and most importantly, it has to work quietly and must not be easily detectable.
This excludes everything with a noticeable impact on the usual functionality of a computer system. Side-channels are perfect for this purpose, as they leak sensitive information about encryption keys to an attacker mainly unnoticed. Anyone looking for signs of huge impact is looking in the wrong place.
Then, backdoors must hide as innocently as possible. For someone looking for vulnerabilities in computer systems a deliberate backdoor must look like an innocent mistake and the knowledge about its existence need to be kept secret by those few people that need to exploit the backdoor.
Fortunately, this is what has gone fundamentally wrong with the catalogue of backdoor tools. A backdoor known to the public, is of far less use, as people can and hopefully will make informed decisions and try to avoid risks, if they have a choice, of course.
How To Weaken A Cryptography Standard
An interesting example how a crypto standard can be weakened deliberately came with the DUAL-EC-DRBG random number generator. Random numbers are essential for the security of every crypto system, so if the output of a random number generator is predictable, the system is essentially broken.
There is a very knowledgeable video in which Professor Edward Frenkel explains how influencing a standard can put someone with intimate knowledge into the pole position when it comes to subverting an encryption process. What the NSA did was persuading the crypto community through NIST to use two large numbers that look totally random to everyone except the NSA to produce secret keys for email encryption. So they didn't actually break the encryption algorithm but they could figure out which key was being used after having observed some output of the random number generator they had backdoored.
For years this backdoor remained undetected because it was a perfect example for an innocent, helpful act of benevolence to provide the two numbers through an approved standard.
Looking At Not-So-Innocent-Looking Backdoors
With the publication of the backdoor tool catalogue there is evidence that for a number of years the NSA and others have implanted backdoors in almost every device they could get their hands on.